I would like to understand what happens with water as it heats and how it may effect quality of brewing coffee (or tea!).

I've heard so often that we should not use water from hot water towers as it 'stands' and looses its oxygen... or that water should not be boiled for too long or it will taste flat. Some have said we should always bring the water to a boil and then let the water cool to the right temperature - more consistent water quality?

As you increase the water temperature, you increase the rate of evaporation. When water evaporates, it does so in the form of pure water vapor.

Therefore, as the water evaporates, the concentration of minerals w/in your brewing water increases (because the water is evaporating, but not the minerals).

The longer water has been standing and/or left at a boil, the higher the concentration of minerals/TDS in your brewing water.

If your hot water tower is in frequent use (i.e. getting fresh water constantly) fluctuating mineral content should be a negligible issue (although I would measure it to be sure!). However, leaving water at a boil without any way of adding in fresh water, would be the worst case -- as it will continue to increase in mineral content (as a %).

Along those lines, I also don't recommend serving the water that is dispensed from a steam boiler on an espresso machine, as it is prone to having a higher mineral content than the brewing water.

I think the recommendation to "bring to a boil, then rest" comes from the notion that, without a thermometer, this is a better/easier way to arrive at the correct brewing temperature.

I've compared press made with zojirushi boilers, a kettle and the newer bunn digital tower - the effect on taste of coffee was present, but subtle. The more interesting thing is to draw water from each let it cool and taste it - and compare water to brewed coffee. The water taste I preferred was my least favourite of the three methods I used to brew. There is a theory with brewing mineral content increases extraction with (iirc) ionic displacement. That is minerals in the water displaces coffee solute - it increases extraction without alterations to the usual time/heat/grind...